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  4. In young's double slit experiment performed using a monochromatic light of wavelength λ, when a glass plate (μ=1.5) of thickness x λ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of x will be:

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Q. In young's double slit experiment performed using a monochromatic light of wavelength $\lambda$, when a glass plate $(\mu=1.5)$ of thickness $x \lambda$ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of $x$ will be:

JEE MainJEE Main 2022Wave Optics

Solution:

image
Path difference at $O =(\mu-1) t$.
If the intensity at $O$ remains (maximum) unchanged, path difference must be $n \lambda$.
$\Rightarrow(\mu-1) t = n \lambda$
$(1.5-1) x \lambda= n \lambda $
$\Rightarrow x =2 n$
For $n=1, x=2$